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HPP Activity 42v1
Modeling Your Circulatory System
Exploration - Your Circulatory System - A Simple Model
"Blood
is
one
of
the
most
interesting
organs
It has two unique properties: it is a liquid and it is always on the move."
in
the
body.
From How the Body Works by John Lenihan.
GE 1.
1. What are the functions of blood flow in your body?
2. When would your body need to increase the blood flow rate?
3. When would some parts of your body need more blood flow than other
parts?.
Here is an engineer's sketch of the blood circulation system of a human body. The circulatory
system can be thought of as a closed-loop circulation system with two pumps. One-way valves
keep the flow uni-directional through the pumps. The pressures are indicated in mm of Hg where
1 atmosphere of pressure is 760 mm of Hg.
Activity Guide
 2010 The Humanized Physics Project
Supported in part by NSF-CCLI Program under grants DUE #00-88712 and DUE #00-88780
HPP Activity 42v1
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GE 2.
1. What are the properties of this system that determine the flow rate of blood?
By what mechanisms does your body regulate its blood flow rate (increase or
decrease the flow rate or change where more of the blood flows). Explain
your ideas.
2. List all of the factors you can think of that might play a role in blood flow
rate. Comment on how you think each factor will contribute. (e.g. thicker
blood – moves slower…)
Activity Guide
 2010 The Humanized Physics Project
HPP Activity 42v1
3
Invention
Don't go on to the next section until you have a class discussion of the important concepts related
to fluid flow and a demonstration of the operation of today's equipment. Be prepared to share
your ideas that your group listed in GE 2.
GE 3.
1. List the classes' predicted factors that affect flow rate and possible
functional (mathematical) dependencies (e.g. flow rate = (constant)*Pressuren)
Factor
Functional relationship
Invention: Flow Rate as a Function of Pressure
Change Pressure
Pressure ~ h
(Keep L and d constant)
Obtain a flow rate apparatus and one tube
determined by your instructor. Be sure to record
ALL values!
GE 4.
1. Describe how you might measure the flow rate of water exiting from the
tube? Discuss your method with your instructor before proceeding.
2. Recall that to do an experiment that tests the relationship between two
variables (factors) you must keep ALL other variables constant during the
experiment. Describe how you will systematically vary the pressure and
measure the resulting flow rate. What variables will you hold constant and
how will you assure they are constant?
Activity Guide
 2010 The Humanized Physics Project
HPP Activity 42v1
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3. Record the values of tube length and tube diameter that you used in this
experiment.
4. Record your data for pressure and flow rate in the table below. Replace
"Variable 1" and "Variable 2" with appropriate names and include the
appropriate units.
Variable 1
Variable 2
5. Copy your data to Excel and graph it. Identify the appropriate mathematical
relationship and determine the best-fit line to your data. Be sure to have Excel
display both the equation and the r2 value and edit the equation so that it has
the proper variables (y and x are not correct!). Paste your graph in the space
below.
6. Describe the physical meaning of this model in words.
Invention: Flow Rate as a Function of Length of the Tube
Activity Guide
 2010 The Humanized Physics Project
Change Length L
(Keep h and d constant)
HPP Activity 42v1
Obtain a set of tubes from your instructor. Be sure
to record the information about the tubes!
GE 5.
1. What variables will you hold constant and how will you assure they are
constant?
2. Record the value of tube diameter, and water height h that you used in this
experiment.
3. Record your data for tube length and flow rate in the table below. Add the
appropriate units.
Length
Flow rate
4. Copy your data to Excel and graph it. Identify the appropriate mathematical
relationship and determine the best-fit line to your data. Be sure to have Excel
display both the equation and the r2 value and edit the equation so that it has
the proper variables (y and x are not correct!). Paste your graph in the space
below.
5. Describe the physical meaning of this model in words.
Activity Guide
 2010 The Humanized Physics Project
5
HPP Activity 42v1
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Change Tube Diameter
L and h constant)
Invention: Flow Rate as a Function of the Inside Diameter of(Keep
the Tube
Obtain from your instructor a set of tubes of equal
length and different diameters. Be sure to record
the values of the things you hold constant.
GE 6.
1. What variables will you hold constant and how will you assure they are
constant?
2. Record the value of tube diameter, and water height h that you used in this
experiment.
3. Record your data for tube length and flow rate in the table below. Add the
appropriate units.
Length
Flow rate
4. Copy your data to Excel and graph it. Identify the appropriate mathematical
relationship and determine the best-fit line to your data. Be sure to have Excel
display both the equation and the r2 value and edit the equation so that it has
the proper variables (y and x are not correct!). Paste your graph in the space
below.
5. Describe the physical meaning of this model in words.
Activity Guide
 2010 The Humanized Physics Project
HPP Activity 42v1
7
Application
GE 7.
1.Poiseuille (1799-1869) was interested in the physics of blood circulation.
He found that the flow rate of a fluid undergoing laminar flow in a cylindrical
tube is:
Flow Rate =  * pressure * (radius)4 / (8 * viscosity* length)
Compare the results of the three different invention activities above to this
equation. Do they appear to agree? Explain.
2.During heavy exercise, the body increases its flow rate 5-10 times greater
than when at rest. Describe different ways that the body might do this?
3.Is increasing blood pressure 5-10 times higher a viable option? Explain.
4.Is decreasing the length of your blood vessels a viable option?
5.The arterioles (small arteries) have sphincter-like muscles around them. How
much would the radius of a blood vessel have to increase to cause a 5 times greater
flow rate?
In fact the body does increase its blood pressure a little to increase the flow rate –
but most of the flow rate increase comes from vasodilatation.
6.Arteries in the human body can be constricted when plaque builds up on the
inside walls. How would this affect the blood flow rate through this artery?
7.If the body wants to keep a constant flow rate, then how might this condition
affect a person's blood pressure? Explain.
Activity Guide
 2010 The Humanized Physics Project
HPP Activity 42v1
8
Application: Using Flow Rate to Determine the Viscosity of a Liquid
Viscosity is a measure of the resistance of a liquid to flow, i.e. for a constant pressure a liquid of
greater viscosity will flow slower than a liquid of lesser viscosity. The relationship is exactly
defined mathematically by an inverse proportion between flow rate and viscosity, holding all
other variables constant. Use the results you obtained above for water to determine the viscosity
of an unknown liquid that you may get from the laboratory instructor.
Procedure: Capture the unknown liquid flowing out of the container for a fixed period of time,
say 1 minute. Have a member of your team pour unknown liquid into the container so the height
of the unknown liquid surface above the exit opening stays constant while you are capturing the
liquid flowing out of the container
GE 8.
1. Determine the viscosity of water from your data above. Ask your instructor for
some clues! Show your calculations.
2. Determine the viscosity of your unknown liquid. Show your calculations.
Activity Guide
 2010 The Humanized Physics Project